Best way to annoy them is do nothing.
- If you do anything it will work against you
- Even if you do nothing they will most likely invent

The ideal solution is to get the DWP to write back to them stating
they "have investigated their complaints and found there was no case
to answer". It may be worth asking them, or asking a solicitor if it
is possible.

An alternative is to get the DWP to confirm in writing there is "no
case to answer" and putting it through their letterbox, or holding it
in reserve if the police ever get involved re harassment. People
behave quite differently and the police can bring up such matters -
deflates such fools most effectively.

I'm afraid it is *very* common.
Smear & slander are now a very common part of neighbours, business,
schools (particularly private, hiding behind charitable trust), even
medical profession (paying full fee for a school when you are an
assisted place and thus should not be allowed to sit all your
subjects, or choose your A-level subjects, or choose university, or
receive references, essentially a charitable trust having a
blacklist).

UK has had 14yrs of hyper-credit - mal-invested in firstly consumption
and secondly in recreating & exceeding the late 1980s housing bubble.
The net result is too many people are "in the ****". I am not, sounds
like you are not either. Smile. Realise financial problems destroy
famillies & lives - often by their own making, creating incredible
frustration which leads to a "collateral lash-out" at any around them
at perceived injustice, fuelling a reinforcing righteous revenge.

Beware it may only take a spark, so worth getting a DWP letter
confirming "no problem" on file as necessary.

Best wishes.